The annual battle to win over the hearts and minds of the Rent Guidelines Board began in earnest yesterday as tenant leaders presented a study claiming more than 40,000 affordable apartments disappeared last year.

“It’s very bad news,” declared Barbara Elstein-Katz, a former official in the city’s Department of Housing, Preservation and Development, who conducted the study.

She found that 16,007 rent-controlled units and 28,128 pre-1947 rent-stabilized units vanished from the regulated rolls, through co-op conversion or vacancy decontrol.

At the same time, 29,408 post-1947 units were added. But the newest units are also highest-priced.

“A family making $70,000 a year cannot find a place to live in New York, unless it’s in subsidized units being developed by the city,” she said.

Landlord representatives maintained that the figures aren’t borne out by the reality.

“Eight million people in New York,” said Jack Freund of the Rent Stabilization Association, which represents 25,000 landlords. “None of them can afford to live here? There is no affordability issue.”